1 Exploratory Data Analysis (EDA)

This document presents an exploratory data analysis of critical elements concentration data, which provide information about the concentration of critical mineral across different areas in Australia that has been normalised using PAAS (Post-Archean Australian Shale) standard. The primary objective of this analysis is to gain a deeper understanding of the data’s structure and key characteristics. Through this, we aim to identify significant trends, correlations, and outliers that may influence the outcomes of the study.


1.1 Data General Characteristics

Our data comprises of 11032 observations and 8 variables. Most of the variables are character type, except for variable Element_Value_ppm, PAAS_value_ppm, and PAAS_normalised_value that are numeric type.

## Classes 'data.table' and 'data.frame':   11032 obs. of  8 variables:
##  $ Project_Name         : chr  "Collingwood Park" "Confidential_B" "Confidential_B" "Confidential_B" ...
##  $ Sample_ID            : chr  "CP-014" "ICP23000472Z291" "ICP23000472Z292" "ICP23000472Z293" ...
##  $ Element_Symbol       : chr  "Ag" "Ag" "Ag" "Ag" ...
##  $ Element_Value_ppm    : num  0.13 0.14 0.11 0.11 0.11 0.11 0.11 0.11 0.15 0.5 ...
##  $ Element_Description  : chr  "Silver" "Silver" "Silver" "Silver" ...
##  $ PAAS_value_ppm       : num  0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 ...
##  $ PAAS_normalised_value: num  2.6 2.8 2.2 2.2 2.2 2.2 2.2 2.2 3 10 ...
##  $ Above_PASS_flag      : chr  "Enriched above background" "Enriched above background" "Enriched above background" "Enriched above background" ...
##  - attr(*, ".internal.selfref")=<externalptr>

The Table 1.1 provide a preview of the data from the first ten observations.

Table 1.1: The first ten observations of the data
Project Name Sample ID Element Symbol Element Value ppm Element Description PAAS value ppm PAAS normalised value Above PASS flag
Collingwood Park CP-014 Ag 0.13 Silver 0.05 2.6 Enriched above background
Confidential_B ICP23000472Z291 Ag 0.14 Silver 0.05 2.8 Enriched above background
Confidential_B ICP23000472Z292 Ag 0.11 Silver 0.05 2.2 Enriched above background
Confidential_B ICP23000472Z293 Ag 0.11 Silver 0.05 2.2 Enriched above background
Confidential_B ICP23000472Z294 Ag 0.11 Silver 0.05 2.2 Enriched above background
Confidential_B ICP23000472Z299 Ag 0.11 Silver 0.05 2.2 Enriched above background
Confidential_B ICP23000472Z300 Ag 0.11 Silver 0.05 2.2 Enriched above background
Confidential_B ICP23000472Z301 Ag 0.11 Silver 0.05 2.2 Enriched above background
Confidential_B ICP23000472Z302 Ag 0.15 Silver 0.05 3.0 Enriched above background
Confidential_C IP23005174R1046 Ag 0.50 Silver 0.05 10.0 Enriched above background


1.2 Descriptive Statistics

In this section, we will provide some generic statistics information about the data, such as min, max, mean, median, and others. The Table 1.2 lay out the details about these informations for each critical element that is included in the data.
Table 1.2: Descriptive Statistics of Elements’ Normalised Value
Element Symbol Element Description min max mean median range q1 q3 iqr sd var skewness kurtosis
Ag Silver 0.100 0.660 0.207 0.180 0.560 0.110 0.272 0.163 0.119 0.014 1.647 5.783
Al Aluminium 7.210 680,000.000 67,579.252 35,000.000 679,992.790 17,000.000 103,000.000 86,000.000 78,592.423 6,176,769,029.641 4.403 34.192
Au Gold 0.001 0.022 0.006 0.006 0.021 0.004 0.008 0.004 0.004 0.000 1.806 7.764
Ba Barium 7.000 10,000.000 609.458 412.500 9,993.000 189.750 653.250 463.500 1,114.878 1,242,952.531 5.997 43.446
Be Beryllium 0.100 18.000 3.377 2.000 17.900 1.000 4.000 3.000 3.401 11.564 1.981 7.156
Bi Bismuth 0.100 3.200 0.468 0.305 3.100 0.200 0.600 0.400 0.419 0.176 3.012 17.818
Cd Cadmium 0.010 0.720 0.125 0.090 0.710 0.050 0.185 0.135 0.109 0.012 2.075 9.839
Ce Cerium 3.600 380.000 61.211 63.050 376.400 31.125 81.375 50.250 38.062 1,448.728 2.362 21.060
Co Cobalt 2.000 134.000 15.400 10.000 132.000 6.000 15.250 9.250 19.268 371.261 3.617 17.661
Cr Chromium 1.000 897.000 36.565 17.000 896.000 11.000 29.000 18.000 86.951 7,560.393 6.622 54.642
Cs Caesium 0.110 31.600 4.915 4.245 31.490 2.445 6.357 3.912 4.188 17.540 2.460 12.858
Cu Copper 1.000 255.000 42.025 47.000 254.000 16.000 60.750 44.750 28.991 840.485 1.617 13.140
Dy Dysprosium 0.400 18.500 5.325 5.310 18.100 3.500 6.715 3.215 2.965 8.790 1.115 5.566
Er Erbium 0.200 11.400 3.222 3.035 11.200 2.000 4.072 2.072 1.875 3.517 1.300 6.383
Eu Europium 0.100 6.840 1.474 1.450 6.740 0.800 1.920 1.120 0.852 0.727 1.295 8.535
Fe Iron 0.190 339,126.000 16,595.088 6,301.000 339,125.810 2,000.000 15,000.000 13,000.000 37,320.398 1,392,812,116.408 5.788 45.053
Ga Gallium 1.300 52.300 21.981 21.950 51.000 12.900 31.625 18.725 11.620 135.019 -0.020 2.148
Gd Gadolinium 0.500 25.100 6.038 5.750 24.600 3.600 7.555 3.955 3.424 11.725 1.380 7.420
Ge Germanium 0.140 70.000 11.970 0.550 69.860 0.292 15.200 14.907 20.849 434.698 1.458 3.653
HREE Ho+Er+Tm+Yb+Lu 1.100 30.600 8.671 8.200 29.500 5.462 10.753 5.290 4.812 23.153 1.374 6.712
Ho Holmium 0.100 3.800 1.081 1.045 3.700 0.700 1.355 0.655 0.613 0.376 1.187 5.962
In Indium 0.020 0.360 0.072 0.050 0.340 0.030 0.100 0.070 0.056 0.003 2.167 9.581
LREE La+Ce+Pr+Nd+Pm+Sm 11.700 554.500 134.275 140.060 542.800 81.100 180.300 99.200 71.054 5,048.606 0.837 6.992
La Lanthanum 3.000 76.200 26.129 27.900 73.200 12.000 36.000 24.000 14.409 207.612 0.155 2.566
Li Lithium 5.000 285.000 47.724 40.000 280.000 15.000 64.500 49.500 39.486 1,559.133 1.860 9.533
Lu Lutetium 0.000 2.000 0.493 0.460 2.000 0.300 0.610 0.310 0.294 0.087 1.420 7.067
MREE Eu+Gd+Tb+Dy+Y 2.700 135.100 41.948 41.410 132.400 24.700 52.330 27.630 23.288 542.320 1.200 5.952
Mn Manganese 1.000 11,230.000 356.239 65.500 11,229.000 19.000 220.500 201.500 1,130.209 1,277,371.401 7.302 66.528
Mo Molybdenum 0.100 20.600 4.456 4.000 20.500 2.000 5.000 3.000 3.292 10.836 2.227 10.237
Nb Niobium 0.500 42.800 7.466 7.765 42.300 4.367 9.418 5.050 4.824 23.273 2.399 16.601
Nd Neodynium 1.700 115.000 29.777 31.750 113.300 14.750 39.525 24.775 16.758 280.838 0.622 4.693
Ni Nickel 1.000 360.000 16.972 7.000 359.000 5.000 13.000 8.000 38.253 1,463.294 5.983 44.099
Pb Lead 0.890 83.450 21.688 21.000 82.560 11.060 28.000 16.940 14.544 211.517 1.344 6.139
Pr Praseodymi 0.400 33.400 7.335 7.750 33.000 3.500 9.848 6.348 4.235 17.935 0.953 7.452
REE La+Ce+Pr+Nd+Sm+Eu+Gd+Tb+Dy+Ho+Er+Tm+Yb+Lu 19.600 611.000 159.328 165.430 591.400 107.100 205.510 98.410 78.891 6,223.739 0.832 6.574
REEY La+Ce+Pr+Nd+Sm+Eu+Gd+Tb+Dy+Ho+Er+Tm+Yb+Lu+Y 23.200 613.000 188.576 193.850 589.800 124.100 237.130 113.030 88.957 7,913.437 0.613 4.600
Rb Rubidium 0.160 299.000 52.910 49.400 298.840 14.300 77.825 63.525 44.400 1,971.391 1.185 5.920
Re Rhenium 0.000 0.003 0.002 0.002 0.003 0.001 0.002 0.002 0.001 0.000 -0.526 1.792
Sc Scandium 2.200 67.800 15.465 16.200 65.600 9.325 19.675 10.350 8.300 68.898 1.108 8.482
Sm Samarium 0.400 21.100 6.394 6.570 20.700 3.450 8.485 5.035 3.532 12.473 0.624 4.173
Sn Tin 1.000 13.000 3.991 3.600 12.000 2.700 4.800 2.100 1.925 3.705 1.671 6.862
Sr Strontium 2.000 1,600.000 334.182 320.500 1,598.000 170.000 467.750 297.750 212.895 45,324.213 1.012 6.965
Ta Thallium 0.100 3.000 0.649 0.690 2.900 0.438 0.800 0.363 0.361 0.131 2.084 14.453
Tb Terbium 0.100 2.930 0.882 0.870 2.830 0.600 1.100 0.500 0.486 0.236 1.103 5.576
Th Thorium 0.470 57.020 12.542 11.850 56.550 5.640 16.200 10.560 9.130 83.359 1.437 6.382
Tl Tantalum 0.030 10.000 1.942 0.715 9.970 0.362 1.510 1.147 3.123 9.753 2.131 5.782
Tm Thulium 0.100 1.800 0.479 0.450 1.700 0.300 0.600 0.300 0.269 0.073 1.551 7.679
U Uranium 0.150 12.000 3.610 3.650 11.850 1.625 5.018 3.393 2.255 5.083 0.541 3.219
V Vanadium 2.000 460.000 111.060 118.000 458.000 50.000 150.000 100.000 71.213 5,071.349 0.961 5.959
Y Yttrium 1.000 100.500 28.110 27.500 99.500 17.000 35.900 18.900 16.811 282.623 1.287 6.443
Yb Ytterbium 0.200 11.900 3.217 3.080 11.700 1.975 4.102 2.128 1.879 3.531 1.259 6.361
Zn Zinc 1.000 307.000 65.378 66.000 306.000 17.000 101.000 84.000 49.645 2,464.655 0.745 4.134
Zr Zirconium 4.000 916.000 175.363 186.000 912.000 93.750 228.000 134.250 112.505 12,657.471 1.419 9.671

The most important statistics from this table is kurtosis. Kurtosis measures the combined weight of the tails of a distribution relative to its centre. In this way, we can use kurtosis as an indicator of the presence of outliers. A high kurtosis values is indicative of outliers. Validating the outliers will be easier with data visualisation, which will be presented in the next section.

The table below represents the descriptive statistics of elements from ME-4ACD81 test that will be used for predictive modelling.


1.3 Distribution Analysis

Next, we are going to analyse the distribution of each critical elements based on their PAAS normalised values. The Figure 1.1 provides insights regarding the spread, central tendency, and potential outliers for each critical element.

Distribution of Critical Elements (Box-Plot)

Figure 1.1: Distribution of Critical Elements (Box-Plot)

As depicted above, there are some key points that we would like to raise, which are:

  • Medians: Most of the elements have their medians close to 0, indicating that the majority of the values are low or concentrated around a lower range. Considering that the threshold to define whether a sample is below/above background is 1, some elements that have median above the threshold are:
    Element Symbol median
    Re 5.000
    Ag 3.600
    Au 3.333
    Mo 2.667
    Bi 2.402
    Li 2.000
    Cu 1.880
    Eu 1.648
    Dy 1.517
    Gd 1.513
    Sm 1.460
    Lu 1.438
    Yb 1.400
    Tm 1.364
    Tb 1.359
    MREE 1.344
    Er 1.320
    Ho 1.306
    U 1.304
    Ga 1.291
    Y 1.250
    Pb 1.235
    Nd 1.221
    Sc 1.191
    REEY 1.151
    REE 1.130
    Th 1.107
    V 1.103
    Pr 1.092
    LREE 1.064
  • Spread and Variability: The elements exhibit varying degrees of spread. For example, Ge shows a wide range with its box stretching from a low value near 0 to a higher value around 10, indicating a large variability. On the opposite side, elements like Mn, Fe, Cr, Co, Rb, Ni, HREE have very narrow IQR, indicating less variability.
  • Outliers: Several elements have significant outliers, as indicated by the dots outside the whiskers of the box plots. For instance, Ge, Bi, Mn, and Ba show notable outliers far from the main data range. Additionally, some elements that was reported from table 1.2, which have high kurtosis are Al, Ba, Bi, Ce, Co, Cr, Cs, Cu, Fe, Mn, Nb, and Ni. These outliers suggest the presence of some unusually high or low values for these elements, which could be of interest for further investigation.
  • Symmetry and Skewness: Some elements like Ge, Bi, and Ag appear to have a right skew, with longer whiskers or outliers extending to the right, indicating that the distribution of their normalised values has a tail on the higher end. Elements like Ga and Sm show a more symmetrical distribution with whiskers extending fairly equally on both sides of the box.
  • Comparison Accross Elements: Ge stands out with a particularly large spread and median, making it an outlier among the elements. Conversely, many rare earth elements (REE, REEY, MREE, LREE, HREE) have relatively low medians and a small spread, indicating that their normalised values are generally low and clustered.
The plot below represents the distribution of elements from ME-4ACD81 test that will be used for predictive modelling.
Distribution of Selected Critical Elements (Box-Plot)

Figure 1.2: Distribution of Selected Critical Elements (Box-Plot)


1.4 Distribution of elements with reference to PASS levels

In this analysis, we are trying to assess all critical elements towards the PAAS standard. To begin with, we start from a high-level distribution across the two main categories that we use in identifying which elements that fall under above/below standard categories. The normalised value will be flagged as “Enriched above background” if it is above 1, while the rest will be flagged as “Below background”. The Figure 1.3 provide the details about this high-level distribution.

The Profile of PASS Categories

Figure 1.3: The Profile of PASS Categories

As depicted in the bar chart, the distribution appears fairly balanced between the two categories, with 5,724 instances classified as “Enriched Above Background” and 5,355 instances classified as “Below Background”. Such a balance highlights the importance of further detailed analysis to understand the factors contributing to this distribution, the significance of enrichment in the context of the dataset, and how these elements behave under different conditions.

Moving on to the element’s level, we will assess how each critical element’s PAAS level, whether they are above/below background value. The Figure 1.4 shows the profile of each sample towards this standard and their respective flags.

Distribution of elements with reference to PASS levels' Concentration

Figure 1.4: Distribution of elements with reference to PASS levels’ Concentration

As can be seen, the majority of normalised value fall within 0 to 10. Some highlight points from this plot are:

  • Ag does not have any normalised PAAS values below background, indicating that coal waste is rich in Ag.
  • HREE concentrations are always below background value.
  • The significant differences in PAAS normalised value for some elements like Ge and Re needs further investigation as to why for a particular element that was sourced from coal and coal byproducts, such big gap could happen. In the later analysis, we will reveal if they are sampled from the same project area or they are actually sampled from different project area.
  • All “below background” samples are actually just fall close to the threshold (between 0 and 1), indicating that coal and coal byproducts are highly potential as sources of these critical elements.
Furthermore, we also analyse how the distribution of the PAAS levels across various Project Area. The Figure 1.5 shows how many elements that was recorded in each project area fall into two categories.
The Profile of Project Area with reference to PASS levels' Concentration

Figure 1.5: The Profile of Project Area with reference to PASS levels’ Concentration

Some key observations from the plot are:

  • The “Confidential_C” project stands out with a substantial number of elements (3,358) categorised as “Enriched Above Background”, significantly outnumbering the “Below Background” category count (1,192). This suggests a considerable concentration of elements that exceeded PAAS standard in this project.
  • Project such as “Fort Cooper”, “Confidential_B” and “Confidential_A” display a more balanced distribution between two categories, indicating a near-equal mix of elements that either meet or fall short of the enrichment criteria.
  • In contrast, several projects, such as “Wandoan”, “Copabella”, “Lake Vermont”, “Collinsville”, “Moorvalle”, “Newlands”, “Metropolitan”, “Rolleston” exhibit a higher count of elements classified as “Below Background”. This implies that these projects have a significant proportion of elements that do not reach the enrichment threshold.
  • A few projects, including “Oaky Creek”, and “Unnamed”, contribute minimally to the overall dataset, with very few elements categorised in either categories.

Lastly, let’s see how is the distribution of each critical element on every project area. The Figure 1.6 below provide this information. As the continuation of the previous analysis, in this part we will focus more on the concentration of each element in each project area. For instance, such insights that we are going to look for are elements that have wide range of concentrations in one project, elements that have above/below background in the same project area.

Distribution of Critical Elements by Each Project Area

Figure 1.6: Distribution of Critical Elements by Each Project Area

As shown by above graphs, some significant insights are:

  • Collinsville: Co has wide range of concentration, which make some samples fall below background, while there is one sample that has high concentration, indicating that in one project area the same element can be significantly different.
  • Confidential_A: the outlier of Tl that was seen in figure 1.1 and figure 1.4 is found here, suggesting high concentration of this element in this project area.
  • Confidential_B: Outliers of multiple elements (Mo, Li, Cr, Ba) that were reported in figure 1.1 are spotted in this project area. This fact is relevant with the figure 1.5 where this project area was the source of many samples in our data. Additionally, we can spot a wide range of Ba concentration, in which one of the sample is categorised as “below background”, while there are two samples that categorised as “above background” with very high normalised value (above 10).
  • Confidential_C: The same conditions as previous project area can be found in this project as well, where many outliers are found here considering many samples were taken in this project. Again, Ba also has a wide range of concentration, a substantial difference is spotted here, where one sample has high concentration value (above 10), while the rest are clustered together between 0 & 5.
  • Fort Cooper: Majority of the elements’ concentration are between 0 & 10. However, we can see some elements which value are beyond 10, such as Mn, Ge, Bi, and Ag.
  • Lake Vermont: Ba records significant concentration differences, where most of its sample are below background but one of them is very high (almost 18).
  • Wandoan: It seems Ge are highly concentrated in this project area, because all of its samples taken from here have concentration beyond 10. This is also revealing where all of those outliers of Ge are located from, as reported in figure 1.1.


1.5 Correlation Matrix plot

Correlation Matrix Plot of Critical Elements

Figure 1.7: Correlation Matrix Plot of Critical Elements

The figure 1.7 shows the relationships between various elements. Some key observations are:

  • Strongly positive correlations: There are numbers of elements that have very strong relationship (above 0.95), such as Er-Dy, Gd-Eu, Ho-Dy, Ho-Er, Pr-Nd, Sm-Nd, Tb-Dy, Tb-Gd, Tb-Ho, Yb-Er, and Yb-Ho. There are also many more elements that have correlation above 0.8.
  • Moderate correlations: Many elements fall between 0.6-0.8, which indicate fairly strong relationships.
  • Weaker Correlations: Elements such as Ba show weaker correlations with most other elements, indicating less consistent co-occurrence or independent behavior within the dataset.This also the case for Sr.
The correlation matrix plot below represents the matrix of elements from ME-4ACD81 test to REE, HREE, and LREE. This is to understand the correlation between all elements to the target variable as part of the predictive modelling.
Correlation Matrix Plot of Selected Critical Elements

Figure 1.8: Correlation Matrix Plot of Selected Critical Elements


1.6 Scatter Plot

In this last section, we are going to dig deeper into critical elements that have correlation value above 0.95 (as mentioned in the previous points). For context, Er, Dy, Gd, Eu, Ho, Pr, Nd, Sm, Tb, and Yb are known as lanthanides series. Lanthanides are a group of the first 15 f-block elements with atomic numbers from 57 to 71. In addition to yttrium, which share many similar chemical properties with the lanthanides, these elements comprise the rare earth elements (REEs) (Mattocks et al., 2021). Their high correlation values are most likely affected due to this fact.

Furthermore, Seredin (2012) suggest that the first suggestions for recovering lanthanides and yttrium (REY) as by-products from coal deposits can be traced back to 20 years ago, following the discovery of coal beds in a Russian Far East (RFE) basin that had high REY content (0.2% - 0.3%). Additional coal seams with comparable or even higher REY concentrations (up to 1.0% in ash) were identified in six coal-bearing basins across the same region. Since then, REY-rich coal has also been discovered in coal basins in various other countries. Thus, the lanthanides are found in coal and coal by-products could be possible because of their association with the materials that make up coal.

Correlated element (Above 0.95)
Strongly Correlated Critical Elements

Figure 1.9: Strongly Correlated Critical Elements

The Figure 1.9 above depicted show correlations between these elements, additional colour dimension was added to differentiate the project areas. In summary, there are many correlations that closely align to each other, as shown by the tight spread of the dot points around the straight line, which are exhibited by Pr & Nd, Gd & Eu, Ho & Er, Tb & Dy, Yb & Er, Sm & Nd, and Sm & Pr plots. In some of the plots, there are a few data points that deviate from the majority of the points. These could be potential outliers or cases where the relationship slightly diverges, which are exhibited by Er & Dy, Ho & Dy, Yb & Dy, Yb & Ho, Tb & Ho, Tb & Gd plots. For Sm & Nd, and Sm & Pr plots even though they are belong to the previous group, but when we look closely from the project area point of view, we can see that the grey dots (which represents ‘Wandoan’) are deviating away from the linear line. This indicates the correlation between them are not strong. Let’s dig deeper into these elements by utilising plots below.

Correlated Critical Elements (Sm, Pr, Nd) in Wandoan

Figure 1.10: Correlated Critical Elements (Sm, Pr, Nd) in Wandoan

As can be seen in the correlation matrix of figure 1.10, in Wandoan, the correlation between Sm and Nd is 0.95, just right at the minimum threshold that we chose. However, Sm and Pr correlation is below 0.95, which contributes to the fact that the points deviate away from the linear line. Considering their correlation value is below our threshold, it’s most likely that Sm and Pr correlation from this project is excluded for the predictive modelling part.

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